An Almost Sure Result on Approximation of Homogeneous Random Field from Local Averages*

The problem of approximation of homogeneous random field from asymmetric local average sampling is considered in this paper. As a general sampling result, a sufficient condition is obtained to ensure the homogeneous random field be approximated from local averages with probability 1, which extended the result for weak sense stochastic process from local averages to homogeneous random field.